top 35% and minimum score

Question

The combined math and verbal scores for students taking a national standardized examination for college admission, is normally distributed with a mean of 880 and a standard deviation of 230. If a college requires a student to be in the top 35 % of students taking this test, what is the minimum score that such a student can obtain and still qualify for admission at the college?

Answer 1

If the tester must be in the top 35% then 65% of the testers are below.

 

Get a z-score chart

https://www.stat.tamu.edu/~lzhou/stat302/standardnormaltable.pdf

 

0.6500 is not on the chart.

0.64803 has a z-score of 0.038

0.65173 has a z-score of 0.039

 

Use extrapolation to determine exact z-score for 0.65.

 

Determining that substitute into the formula

 

z = (X - μ) / σ, z = z-score, X = test score, μ = mean, σ = standard deviation

and solve for X.